When I have all the desktop showing (referred to in control center-->keyboard shortcuts as "Toggle Showing Desktop"), which effectively minimizes all windows, I find that I can't open a new window of any kind without the other windows popping back up. It seemingly undoes my command to show the desktop. I realize that the system probably doesn't treat "toggle showing desktop" as though I actually clicked the minimize button on every window, but the effect is the same to me (that's why I use the command in the first place); so I expect those windows to stay down until I bring them back individually, and find it annoying that they all pop up when I open some new window. Is there anything I can do about it?

Show desktop is designed to show you your desktop - that is all. If you open a new window then you are telling the computer that you have finished viewing the desktop, so it seems to be returning back to the way it was. You are better off switching to another workspace and opening your new window there.

It works as you desire on my system and on Windows, so maybe you have other issues.